A piece of fact-based historical uplift that flirts with sappiness but never succumbs, “Hidden Figures” is a late addition to the 2016 awards race.

The story it tells — largely unknown until the film’s publicity drive kicked in a few weeks ago — is kinda jaw dropping. And the three lead performances instantly land on the list of Oscar contenders.

During the early days of the American space program — back when a mechanical computer took up an entire floor of an office building — NASA hired two dozen mathematically gifted African American women to perform complex calculations using nothing more than their brains and slide rules.

These women were referred to as “computers” — that was their official job designation.

Despite being second-class citizens both on and off the job, they made possible John Glenn’s breakthrough orbital flight and gave the U.S.A. a fighting chance in the space race.

Writer/director Theodore Melfi (he was behind the sublimely funny Bill Murray starrer “St. Vincent”) balances the private stories of three of these women against the grand historic sweep of those years. The film works equally well as a satisfying celebration of personal triumph and as a symbol of national pride.

The screenplay (with Allison Schroeder) wastes no time in illustrating the times. Three “computers” are on their long daily commute to their jobs in north Virginia when their car breaks down. The white highway patrolman who investigates their stalled vehicle at first exhibits the overt racism of the times. Only when he learns that the three are helping Uncle Sam beat the Commies to the stars does he drop the attitude and ensure they are sent safely on their way.

Once at work, the women must put up with more crap. The space program (it wouldn’t take the name NASA for several years) and its white management practice what might be called “racism with a tight smile.”

The African American women work in their own building separate from everyone else. There is minimal interaction between them and the engineers and scientists who daily shower them with mathematical problems. Like the field hands of a Southern plantation, they produce the wealth but get none of the credit.